MATH 10A Lecture Notes - Lecture 17: Unit Circle, Hypotenuse, Quotient Rule
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Example: find the intervals where is concave up and concave down. Solution: f " (x)= f " " (x)= f " " (x)= f " " (x)= f " " (x)= . 3 x= f f"" + - + Height of triangle on unit circle = sin(x +h) sin (x) Hypotenuse on unit circle = 1(h) lim h 0 d dx. Example: f (x)=sin (x2 x) f " (x)=cos(x2 x )(2x 1) Example: g(x)=xcosx g "(x)=x ( sinx)+1(cosx) g "(x)= xsinx +cosx. Example: f (t)=esin(3t) f " (t)=esin(3t ) cos(3t) 3. [tanx]= d dx d dx d dx d dx. = 1 co s2 x co s2 x (cosx)(cosx) (sinx)( sinx) Example: f (x)=tan(e x) co s2( x ) f " (x)= 1 e ex co s2 f " (x)= ex. Example: g(t)=t3(tant ) g "(t)=t3 1 co s2 t. Find an equation for the tangent line to y=sinx at x= . 3 y y y= 1 x .
